select the correct answer. josh has $500 in his savings account. he purchases home theater equipment for…

select the correct answer. josh has $500 in his savings account. he purchases home theater equipment for $1,550. the store offers him a $1,550 interest - free loan. he needs to pay $80 per month until the purchase is paid for. every month, josh pays the $80 loan payment and also deposits $25 into his savings account. in how many months will he have as much in savings as he owes on the home theater equipment? a. 8 months b. 10 months c. 20 months d. 24 months

select the correct answer. josh has $500 in his savings account. he purchases home theater equipment for $1,550. the store offers him a $1,550 interest - free loan. he needs to pay $80 per month until the purchase is paid for. every month, josh pays the $80 loan payment and also deposits $25 into his savings account. in how many months will he have as much in savings as he owes on the home theater equipment? a. 8 months b. 10 months c. 20 months d. 24 months

Answer

Explanation:

Step1: Calculate net monthly savings

Josh deposits $25$ per month into savings. His net - monthly increase in savings is $25$ dollars.

Step2: Calculate the amount he owes

The cost of the home - theater equipment is $1550$ and he has $500$ in savings. So, the amount he owes is $1550 - 500=1050$ dollars.

Step3: Set up an equation to find the number of months

Let $m$ be the number of months. The amount he saves in $m$ months is equal to the amount he owes. The amount he saves in $m$ months is $25m$. We set up the equation $25m=1050$.

Step4: Solve the equation for $m$

Dividing both sides of the equation $25m = 1050$ by $25$, we get $m=\frac{1050}{25}=42$ (This is wrong. Let's correct the logic). The correct way: The amount he owes after buying is $1550 - 500=1050$. Each month, his debt decreases by $80$ (loan payment) and his savings increase by $25$. The net - change in the difference between his debt and savings per month is $80 + 25=105$. Let $n$ be the number of months. We set up the equation $105n=1050$. Dividing both sides by $105$, we get $n = 10$.

Answer:

B. 10 months